In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and cubic B-spline quasi-interpolation operator. Error analysis shows that our method produ...

4 Generalized and Optimized Spline Calculation 8 4.1 Multidimensional Array Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Condensing Matrix Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.3 Eliminating Nested Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.4 Reduction of Product Tens...

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C 2 -continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large p...

B-splines provide an accurate and efficient method for interpolating regularly spaced data. In this paper, I study the applicability of B-spline interpolation in the context of the inverse interpolation method for regularizing irregular data. Numerical tests show that, in comparison with lower-order linear interpolation, B-splines lead to a faster iterative conversion in under-determined proble...

Arbitrary ratio sampling rate conversion (SRC) structure using B-spline interpolation is proposed for software defined radio (SDR) in this paper. By combining SRC with SDR’s transmitter/receiver filter, the constraint on SRC reconstruction filter can be relaxed, and an overall computational reduction can be achieved. The mixedwidth B-spline is introduced so that both antiimaging and anti-aliasi...

This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and Hadwiger 05], which are hard-wired on the GPU and therefore very fast. Here it is demonstrated tha...

An algorithm is presented that constructs a C 2-continuous B-spline quaternion curve which interpolates a given sequence of unit quaternions on the rotation group SO(3). The de Casteljau type construction method of B-spline curves can be extended to generate B-spline quaternion curves Sch92]; however, the B-spline quaternion curves do not have C 2-continuity in SO(3). The authors KKS94a] recent...